Spheroidal Wave Functions in Electromagnetic

The flagship monograph addressing the spheroidal wave function and its pertinence to computational electromagneticsSpheroidal Wave Functions in Electromagnetic Theory presents in detail the theory of spheroidal wave functions, its applications to the analysis of electromagnetic fields in various spheroidal structures, and provides comprehensive programming codes for those computations.The topics covered in this monograph include: Spheroidal coordinates and wave functions Dyadic Greena??s functions in spheroidal systems EM scattering by a conducting spheroid EM scattering by a coated dielectric spheroid Spheroid antennas SAR distributions in a spheroidal head model The programming codes and their applications are provided online and are written in Mathematica 3.0 or 4.0. Readers can also develop their own codes according to the theory or routine described in the book to find subsequent solutions of complicated structures.Spheroidal Wave Functions in Electromagnetic Theory is a fundamental reference for scientists, engineers, and graduate students practicing modern computational electromagnetics or applied physics.

LE-WEI LI, PhD, is Deputy Director of the Antenna and Scattering Laboratory and Electromagnetics Research Group at the National University of Singapore. He is a senior member of the IEEE, an editorial board member of Journal of Electromagnetic Waves and Applications, and the author of Dyadic Greens Functions in Inhomogeneous Media and Electromagnetic Theory of Complex Media.

Preface

v

Acknowledgments

vii

Introduction

1

(12)

Overview

1

(3)

EM Scattering by Spheroids

4

(1)

Spheroidal Antenna

5

(2)

EM Radiation in Dielectric Spheroids

7

(1)

Oblate Spheroidal Models

8

(1)

Spheroidal Cavity System

9

(1)

Spheroidal Harmonics and Mathematica Software

10

(3)

Spheroidal Coordinates and Wave Functions

13

(48)

Spheroidal Coordinate Systems

13

(4)

Spheroidal Scalar Wave Functions

17

(1)

Spheroidal Angular Harmonics

18

(4)

Series Representation in Terms of Associated Legendre Functions

18

(2)

Power Series Representation

20

(2)

Eigenvalues λmn and Expansion Coefficients drmn

22

(5)

Case I:|c|2 ≤ 1000

23

(3)

Case II:|c|2 > 1000

26

(1)

Spheroidal Radial Harmonics

27

(8)

Series Representation in Terms of Spherical Bessel Functions

27

(2)

Proportional Relations of Angular and Radial Functions

29

(1)

Power and Legendre Functional Series Representations

30

(5)

Derivatives of Spheroidal Functions

35

(1)

Derivatives of Angular Functions

35

(1)

Derivatives of Radial Functions

35

(1)

Numerical Calculations and Discussion

36

(8)

Mathematica Source Codes

36

(1)

Geometrical Features of Spheroidal Functions

37

(1)

Tabulated Numerical Data: New Results and Comparison

37

(7)

Spheroidal Vector Wave Functions

44

(17)

Dyadic Green's Functions in Spheroidal Systems

61

(28)

Dyadic Green's Functions

61

(2)

Fundamental Formulation

63

(3)

Unbounded Dyadic Green's Functions

66

(4)

Method of Separation of Variables

66

(1)

Unbounded Scalar Green's Function

67

(1)

Appropriate Spheroidal Vector Wave Functions for Construction of DGFs

68

(1)

Unbounded Green's Dyadics

69

(1)

Scattering Green's Dyadics

70

(3)

Scattering Green's Dyadics in the Inner Region (f = 1)

71

(1)

Scattering Green's Dyadics in the Intermediate Regions (2 ≤ f ≤ N -1)

71

(1)

Scattering Green's Dyadics in the Outer Region (f = N)

72

(1)

Determination of Scattering Coefficients

73

(13)

Nonorthogonality and Functional Expansion

73

(3)

Matrix Equation Systems

76

(10)

Convergence of the Solution

86

(3)

EM Scattering by a Conducting Spheroid

89

(26)

Geometry of the Problem

89

(1)

Incident and Scattered Fields

89

(3)

Transformation of Incident Fields to Scattered Fields

92

(11)

Imposing the Boundary Conditions

92

(1)

TE Polarization for Oblique Incidence

93

(6)

TM Polarization for Oblique Incidence

99

(2)

Fields at Axial Incidence

101

(1)

TE Fields with Incidence Angle 90°

102

(1)

Far-Field Expressions

103

(3)

Numerical Computation and Mathematica Source Codes

106

(2)

Results and Discussion

108

(7)

EM Scattering by a Coated Dielectric Spheroid

115

(30)

Geometry of the Problem

115

(2)

Incident, Transmitted and Scattered Fields

117

(2)

Relationship between Incident and Scattered Fields

119

(11)

Boundary Conditions

119

(1)

TE Polarization for Nonaxial Incidence

119

(9)

TM Polarization for Nonaxial Incidence

128

(2)

Fields at Axial Incidence

130

(1)

Numerical Computation and Mathematica Source Code

130

(2)

Results and Discussion

132

(13)

Spheroidal Antennas

145

(46)

Introduction

145

(1)

Prolate Spheroidal Antenna

146

(6)

Antenna Geometry

146

(1)

Maxwell's Equations for the Spheroidal Antenna

146

(2)

Auxiliary Scalar Wave Function

148

(1)

Imposing the Boundary Conditions

149

(1)

Far-Field Expressions

150

(1)

Numerical Computations and Mathematica Code

150

(1)

Results and Discussion

151

(1)

Dielectric-coated Prolate Spheroidal Antenna

152

(16)

Coated Dielectric Antenna Geometry

152

(6)

Obtaining the Auxiliary Wave Functions

158

(3)

Imposing the Boundary Conditions

161

(1)

Numerical Computations

162

(1)

Mathematica Code

163

(2)

Results and Discussion

165

(3)

Prolate Spheroidal Antenna enclosed in a Confocal Radome

168

(23)

Geometry of the Antenna with Radome

168

(6)

Obtaining the Auxiliary Wave Functions

174

(1)

Imposing the Boundary Conditions

174

(2)

Numerical Computations

176

(1)

Mathematica Code

177

(2)

Results and Discussion

179

(12)

SAR Distributions in a Spheroidal Head Model

191

(36)

Introduction

191

(1)

Multilayered Prolate Spheroidal Head Model

192

(2)

Formulation of the Problem

194

(2)

Expansions of EM Fields Using Spheroidal Wave Functions

194

(1)

EM Boundary Conditions for Multispheroidal Interfaces

195

(1)

Specific Absorption Rate

195

(1)

Numerical Computation

196

(1)

Results and Discussion

197

(12)

Effects on Wire Antennas Due to the Presence of the Multilayered Spheroid

209

(9)

Numerical Results and Discussion

218

(9)

Analysis of Rainfall Attenuation Using Oblate Raindrops

227

(18)

Introduction

227

(3)

Rainfall Attenuation

227

(1)

Raindrop Models in Different Sizes

228

(1)

Oblate Spheroidal Raindrops

229

(1)

Problem Formulation

230

(8)

Geometry of the Problem

230

(1)

Definition of the EM Field

230

(4)

Boundary Conditions and Solution of Unknowns

234

(3)

Total Cross Section

237

(1)

Size Parameters of Raindrops

238

(1)

Radius-Independent Oblate Spheroid Raindrop

238

(1)

Radius-Dependent Oblate Spheroid Raindrop

238

(1)

Numerical Calculation and Results

239

(6)

EM Eigenfrequencies in a Spheroidal Cavity

245

(10)

Introduction

245

(1)

Theory and Formulation

246

(3)

Background Theory

246

(1)

Derivation

247

(2)

Numerical Results for TE Modes

249

(3)

Numerical Calculation

249

(1)

Results and Comparison

250

(2)

Numerical Results for TM Modes

252

(2)

Numerical Calculation

252

(1)

Results and Comparison

252

(2)

Discussion

254

(1)

Appendix A Expressions of Spheroidal Vector Wave Functions

255

(8)

Appendix B Intermediates Imnt,l (C) in Closed Form

263

(10)

B.1 The Case where m ≥ 1

264

(5)

B.2 The Case where m = 0

269

(4)

Appendix C uq(i),t and vq(i),t Used in the Matrix Equation System

273

(4)

References

277

(15)

Index

292

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Spheroidal Wave Functions in Electromagnetic Theory

Summary

Author Biography

Table of Contents

Supplemental Materials